weyl inequality
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2021 ◽  
Vol 202 ◽  
pp. 112147
Author(s):  
Sean McCurdy ◽  
Raghavendra Venkatraman


2020 ◽  
pp. 1-7
Author(s):  
Rajendra Bhatia ◽  
Tanvi Jain

Abstract If A is a real $2n \times 2n$ positive definite matrix, then there exists a symplectic matrix M such that $M^TAM=\text {diag}(D, D),$ where D is a positive diagonal matrix with diagonal entries $d_1(A)\leqslant \cdots \leqslant d_n(A).$ We prove a maxmin principle for $d_k(A)$ akin to the classical Courant–Fisher–Weyl principle for Hermitian eigenvalues and use it to derive an analogue of the Weyl inequality $d_{i+j-1}(A+B)\geqslant d_i(A)+d_j(B).$



2018 ◽  
Vol 29 (12) ◽  
pp. 1850086 ◽  
Author(s):  
Kais Smaoui

The purpose of this paper is to formulate and prove an analogue of the classical Heisenberg–Pauli–Weyl uncertainty inequality for connected nilpotent Lie groups with noncompact center. Representation theory and a localized Plancherel formula play an important role in the proof.





2005 ◽  
Vol 134 (3) ◽  
pp. 731-735 ◽  
Author(s):  
Aicke Hinrichs






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